As we know the light rays or photons would be deviated from their
straight way when they pass close to the massive object such as
black holes. This deflection of light rays is known as gravitational
lensing. This gravitational lensing is one of the applications and
results of general relativity [1]} and is used as an
instrument in astrophysics, because it can help us to extract the
information about stars. In 1924 Chwolson pointed out that when a
star(source), a deflector(lens) and an observer are perfectly
aligned, a ring-shape image of the star appears which is called
'Einstein ring'. Other studies have been led by Klimov, Liebes,
refsdal and Bourassa and Kantowski [2]}. Klimov
investigated the lensing of galaxies by galaxies [3]}, but
Liebes
studied the lensing of stars by stars and also stars
by clusters in our galaxy [4]}. Refsdal showed that the
geometrical optics can be used for investigating the gravitational
lenses properties and time delay resulting from it
[5]}, [6]}.
The gravitational lensing
has been presented in details in [7]} and reviewed by
some papers (see for examples [8]}-[9]}). At
this stage, the gravitational lensing is developed for weak field
limit and could not describe some phenomena such as looping of light
rays near the massive objects. Hence, scientists started to study
these phenomena from another point of view and they proposed
gravitational lensing in a strong field limit. When the source is
highly aligned with lens and the observer, one set of infinitive
relativistic "ghost" images would be produce on each side of black
hole. These images are produced when the light rays that pass very
close to black hole, wind one or several times around the black hole
before reaching to observer. At first, this phenomenon was proposed
by Darwin [10]} and revived in Refs.
[11]}-[12]}. Darwin
proposed a surprisingly easy formula for the positions of
the relativistic images generated by a Schwarzschild black hole.
Afterward several studies of null geodesics in strong gravitational
fields have been led in literatures: a semi-analytical investigation
about geodesics in Kerr geometry has been made in [13]},
also the appearance of a black hole in front of a uniform background
was studied in Refs. [14]}, [15]}. Recently, Virbhadra and
Ellis formulated lensing in the "strong field limit" and obtain the
position and magnification of these images for the Schwarzschild
black hole [16]}, [17]}. In Ref [18]}, by
an alternative formulation, Frittelli, Kiling and Newman attained
an exact lens equation, integral expressions for its solutions, and
compared their result with Virbhadra and Ellis. Afterwards, the new
method was proposed by Bozza et al. in which they revisited the
schwarzschild black hole lensing by retaining the first two leading
order terms [19]}. This technic was used by Eiroa, Romero
and Torres to study a Reissner-Nordstrom black hole [20]} and
Petters to calculate relativistic effects on microlensing events
[21]}. Finally, the generalization of Bozza's method for
spherically symetric metric was developed in [22]}. Bozza
compared the image patterns for several interesting backgrounds and
showed that by the separation of the first two relativistic images
we can distinguish two different collapsed objects. Further
development for other black holes can be found in [23]}-[24]}. Several interesting
studeies are devoted to lensing by naked singularities [25]}, [26]},
Janis-Newman-Winicour metric [22]} and role of scaler field
in gravitational lensing
[28]}. In Ref [28]},
Virbhadra et al. have considered a static and circularly symmetric
lens characterized by
mass and scalar charge parameter and investigated the lensing for different values of charge parameter.
